True, but -- there are ways. One of the good measurres of an Ivy League school (and schools that wish to be thought of as "ivys") is that if you can get in, you can afford it. Now if tall blonde Betty happens to be such a good volleyball player that the volleyball coach will put her on his list of sidedoor entries, the parents can certainly feel that the money they invested in Betty's volleyball development is paid back by the discount they got from the full price, perhaps based on the fact that they have no savings left after financing Betty's training.
The Varsity Blues scandal of the last few years was a different side of the coin. Parents who could easily afford to pay the full retail price of any school, Ivy or not, had enough money to pry open that side door despite a lack of athletic talent.
And then there is the old legend of Ned Harkness in his days as Cornell ice hockey coach. He took advantage of the fact that Cornell housed the NY State Agriculture College in a cooperative agreement with the Regents of the University of New York, which resulted in one of the best veterinary medicine schools in the country. The ag school students overlapped with the mainline Cornell students in housing, many of the classes, and all student social activities, including athletic teams playing under the Cornell banner. While Cornell itself gave out no athletic scholarships, the Ag College was not so constrained, so a lot of Canadian farmboys brought their hockey skates south to study animal husbandry. Savvy fans at rival schools carried cowbells to games when Cornell visited.